Judge Brett Kavanaugh, President Trump’s nominee for the Supreme Court, in Washington in July. Over his decades-long legal career, Judge Kavanaugh has argued in favor of religious freedom in education.CreditCreditErin Schaff for The New York Times

WASHINGTON — Judge Brett M. Kavanaugh, in a speech last year, gave a strong hint at his views on taxpayer support for religious schools when he praised his “first judicial hero,” Justice William Rehnquist, for determining that the strict wall between church and state “was wrong as a matter of law and history.”

Mr. Rehnquist’s legacy on religious issues was most profound in “ensuring that religious schools and religious institutions could participate as equals in society and in state benefits programs,” Judge Kavanaugh, President Trump’s nominee to succeed Justice Anthony M. Kennedy on the Supreme Court, declared at the American Enterprise Institute, a conservative research organization.

Words like that from a Supreme Court nominee are breathing new life into the debate over public funding for sectarian education. Educators see him as crucial to answering a question left by Justice Kennedy after the Supreme Court ruled it unconstitutional for the state of Missouri to exclude a church-based preschool from competing for public funding to upgrade its playground: Can a church-school playground pave the way for taxpayer funding to flow to private and parochial schools for almost any purpose?

Over his decades-long legal career, Judge Kavanaugh has argued in favor of breaking down barriers between church and state. He has filed friend-of-the-court briefs in support of school prayer and the right of religious groups to gain access to public school facilities. He was part of the legal team that represented former Gov. Jeb Bush of Florida in 2000 when he defended a school voucher program that was later ruled unconstitutional. The program had used public funds to help pay the tuition of students leaving some of the state’s lowest-performing schools for private or religious schools.

School voucher champions see Judge Kavanaugh as a critical vote in overturning longstanding constitutional prohibitions, often called Blaine Amendments, that outlaw government funding of religious institutions in more than three dozen states. The amendments have been used to challenge programs that allow taxpayer funding to follow children to private and parochial schools, and are seen as the last line of defense against widespread acceptance of school voucher programs.

But the court’s ruling was narrow. With Justice Kennedy joining the majority opinion, the justices included a footnote to the Trinity case clarifying, “This case involves express discrimination based on religious identity with respect to playground resurfacing. We do not address religious uses of funding or other forms of discrimination.”

“They didn’t want to settle the question once and for all, and I anticipate a case is going to come forward to test footnote three,” said Michael Q. McShane, the director of national research at EdChoice, a pro-voucher group. “It seems that he would be a pretty solid vote.”

Judge Kavanaugh’s nomination has rallied both sides of the voucher debate.

In a piece called “Mr. Kavanaugh, tear down this wall,” a fellow at the conservative Thomas B. Fordham Institute, Dale Chu, expressed hope that “one of the most contentious issues within education policy may once again have its day in court.”

“If we’re serious about educational equity, it seems to me that we need to get past religion in schools as a nonstarter,” Mr. Chu wrote.

Scott Sargrad, the managing director of primary and secondary education policy at the liberal Center for American Progress, wrote that while Education Secretary Betsy DeVos’s school voucher agenda has not gained traction, “if confirmed, Kavanaugh may be the solution to her problems.”

“It is not a stretch to imagine a series of 5-to-4 decisions that slowly decimate public education in favor of voucher schemes,” Mr. Sargrad wrote.

Ms. DeVos has been among the most vocal critics of the legal prohibitions on parochial school vouchers. In a speech to leaders of religious schools this year, she called the prohibitions — born out of anti-Catholicism — “the last acceptable prejudice” that “should be assigned to the ash heap of history.”

Ms. DeVos has stalled in her efforts to create a $1 billion school voucher program, but after the Trinity decision, she has moved to loosen regulations that exclude religious colleges from participating in federal aid programs.

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The Supreme Court issued an opinion last year declaring it unconstitutional for the state of Missouri to exclude a church-based school from competing for public funding to upgrade its playground.CreditStephen Crowley/The New York Times

But for David McGuire, a nontraditional-school advocate and principal of a charter school in Indianapolis, Mr. Kavanaugh’s nomination is complicated.

Judge Kavanaugh has said his upbringing by a public-school teacher imparted lessons about racial and economic inequality, and inspired him to embrace parents’ rights to choose schools for their children. As a young boy, Mr. McGuire recalled using his grandmother’s address to attend a better school outside his neighborhood.

But as a black man leading a majority black school, Mr. McGuire also has been fighting to safeguard students’ civil rights, which he believes Mr. Trump seeks to eradicate. And Judge Kavanaugh’s record gives him pause on that front. The nominee has argued against race-conscious voting policies, using the same arguments that the Trump administration has used to undo policies aimed to fight systemic discrimination. In 1999, Mr. Kavanaugh was a co-author on an amicus brief in support of the Center for Equal Opportunity, a group that opposes affirmative action, with Robert H. Bork, who was openly critical of the 1964 Civil Rights Act.

“I’m representing a school that’s trying to bring hope to a community,” Mr. McGuire said. “And there’s a Supreme Court nominee who tugs at the heart strings of what I’m trying to do who has aligned himself with individuals, and a president, who are trying to wipe out the rights of whole demographics of folks. It puts you between a rock and a hard place.”

There are no voucher cases pending before the Supreme Court, but relevant cases are moving through lower courts: a case in New Mexico, which the Supreme Court kicked back for reconsideration after Trinity, involves the exclusion of religious and private schools from a state textbook-lending program.

Just last week, the Puerto Rico Supreme Court ruled in favor of a government-sponsored voucher program, rejecting an argument from the teachers union that the program violated a “support clause” in the island’s Constitution that prohibits support of nonpublic schools.

The conservative group that represented the families in Puerto Rico, the Institute for Justice, has litigated more than 20 educational choice cases, and has another pending before the Montana Supreme Court. In that case, the state Department of Revenue prohibited families from participating in a tax credit scholarship program if they planned to use the scholarship at religious schools.

On Tuesday, the institute used the Trinity case to petition a United States District Court in Washington to challenge the state’s Blaine Amendment. The group is representing a private Christian academy that was excluded as an option for college students who qualify to earn financial aid through the work-study program.

“This program has all the hallmarks of a school choice program, because it’s a financial-aid program designed to benefit students,” said Michael Bindas, a senior lawyer for the Institute for Justice. “It operates on private choice just the way school programs do. It’s about the fundamental principle that government has to be neutral, not hostile, toward religion.”

Judge Kavanaugh’s record suggests he believes the separation of church and state has been applied too liberally in public school settings.

In a 1999 school prayer amicus brief, he argued in favor of a high school in Santa Fe, Tex., allowing students to lead an invocation, even if it included God, before varsity football games.

“If the student speaker must avoid ‘prayer,’ as respondents demand, does that mean all references to God?” he wrote. “What about references to the ‘Father’? The ‘Father above’? Must the student avoid a reference to ‘our creator’? Can the student ask the crowd to observe a moment of silence for the crowd ‘to pray’ as they wish?”

The Supreme Court ruled the prayers unconstitutional, with Justice Kennedy in the majority.

In another case, Judge Kavanaugh and Justice Kennedy came down on the same side when the Supreme Court ruled that a New York school district could not prohibit a Christian group, the Good News Club, from using its facilities.

In a 2000 amicus brief, Judge Kavanaugh argued that the school district’s policy was discriminatory and would force religious people to “water down their beliefs and hide the religiosity of their message in order to satisfy a government administrator.”

Supporters of a strict division between church and state say that Judge Kavanaugh and Justice Kennedy do hold profoundly different views and that Judge Kavanaugh’s confirmation would reshape public education.

“Justice Kennedy was very protective of schoolchildren, and believed that failing to shield them from religious coercion was an attack on their rights,” said Rachel K. Laser, the executive director of Americans United for Separation of Church and State, which compiled a report on Mr. Kavanaugh’s record on church and state issues. “Judge Kavanaugh believes that shielding children from religious coercion is an attack on religion.”

Correction:

An earlier version of this article misstated the surname of a senior attorney for the Institute for Justice. He is Michael Bindas, not Binder.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Religious Schools See a Champion in Kavanaugh. Order Reprints | Today’s Paper | Subscribe